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Prediction is an essential operation in many image processing applications, such as object detection and image and video compression. When the images are modeled as Gaussian, the optimal predictor is linear and easy to obtain. However, image texture and clutter are often non-Gaussian, and, in such cases, optimal predictors are difficult to obtain. In this paper, we derive an optimal predictor for an important class of non-Gaussian image models, the block-based multivariate Gaussian mixture model. This predictor has a special nonlinear structure: it is a linear combination of the neighboring pixels, but the combination coefficients are also functions of the neighboring pixels, not constants. The efficacy of this predictor is demonstrated in object detection experiments where the prediction error image is used to identify "hidden" objects. Experimental results indicate that when the background texture is nonlinear, i.e., with fast-switching gray-level patches, it performs significantly better than the optimal linear predictor.